McCubbin's Theorems of Tesseract-Space

In 1931, Albert McCubbin published his 3 Theorems of Tesseract-Space. The theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself. The third theorem, states that based on the lack of a constant axioms, along different "planes of thought" or existence, it is entirely possible for contradictory information and even objects to exist in the same plane of axis.


The first theorem states that:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory

The second theorem can be stated as follows:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

The third theorem can be stated as follows:

Any generated set of random factors and axioms, remaining separate from each other, generated in formal theory, can allow for seemingly contradictory objects that are true in existence, but cannot be proven in theory


What is frightening to many mathematicians and scientists is not only the implications of his work in regards to the absence of ultimate and universal truths, but also the idea that there are objects and possible intelligences that are beyond the scope of knowledge. It should be noted that McCubbin committed suicide on December 12, 1932. His suicide has sparked many rumors within the scientific and religious community. Some theologians have suspected that McCubbin committed suicide when confronted with the existentialist dilemma of the "greater unknown and its influence on humanity".

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License